<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">seq</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>assume </b><a NAME="E1:16"/>
<font color="Maroon">seq</font> is <a href="seq_2.html#V1">bounded_above</a>
 ;<br/>

<a NAME="E2:16"/><b>then </b>
( not  <a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font> is <a href="xboole_0.html#V1">empty</a> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font> is <a href="seq_4.html#V1">bounded_above</a> )
 
<b>by </b><i>, <a class="ref" href="setlim_1.html#T8">SETLIM_1:8</a></i>;<br/>
<b>then </b> <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font></span>)</span> = 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K3">inf</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K4">-</a> <span class="p3">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="pscomp_1.html#T18">PSCOMP_1:18</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K3">inf</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p3">(<span class="default"><a href="partfun3.html#K6">-</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
;<br/>
<a NAME="E4:16"/><b>then </b>
 <a href="rinfsup1.html#K1" target="_self">sup</a> <font color="Maroon">seq</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K3">inf</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p3">(<span class="default"><a href="partfun3.html#K6">-</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E5:16"/>
 <a href="rinfsup1.html#K1" target="_self">sup</a> <font color="Maroon">seq</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="rinfsup1.html#K2" target="_self">inf</a> <span class="p2">(<span class="default"><a href="partfun3.html#K6">-</a> <font color="Maroon">seq</font></span>)</span></span>)</span>
 ;<br/>


</div>
